Class Of Linear Multivariable Systems Research Articles

On proper and stable stabilising controllers for a class of linear multivariable systems

In this paper, we examine the problems of existence and computation of proper and stable stabilising compensators in the feedback path of a special class of linear time-invariant multivariable systems characterised by a strictly proper transfer function matrix. For the class of systems that are ‘square’, i.e. have the same number of inputs and outputs and have no zeros in the closed right half complex plane and the class of ‘non-square’ systems that include a ‘square’ subsystem that has no zeros in the closed right half complex plane we present a sufficient condition for the existence and computation of proper stabilising (pole placing) compensators which in certain cases that depend on the transfer function matrix of the system can be chosen to be stable.

Robust output regulation for a class of linear multivariable systems

In the design of robust regulators, the solution of an H ∞-norm optimization problem of the formmin Q ϵ R, H ∞ ∥T 11 −T 12QT 21 ∥ ∞ is needed to get an optimal controller. A difficulty in doing this is that T 12(j ω) will be singular at the poles of the external signals. In [11], a lower bound for this norm has been found. In this paper, it will be shown that, for stable plants, this bound is an infimum and can be approximated as near as possible. Thus, a necessary and sufficient condition for robust regulation is found for a class for a class of linear MIMO systems. Moreover, if the external signals are step functions, an H ∞-optimal controller can be obtained.

Shaping of the output response in a class of linear multivariable systems

A state feedback controller is designed to regulate, as desired, the output response of minimum-phase linear multivariable square plants with CB having full rank (B: input matrix and C: output matrix). Properties of the controller are given and an example is worked out for illustration.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Singular perturbation analysis of the step-response matrices of a class of linear multivariable systems

Singular perturbation methods are used to demonstrate that the step-response matrices of linear multivariable systems containing small ‘parasitic” elements have a distinctive structure which guarantees the robustness of both non-adaptive and adaptive controllers for such systems incorporating step-response matrices. The significance of these results in relation to the modelling of multivariable plants with ‘fast” actuators and sensors is illustrated, and their validity is demonstrated by considering a typical gas-turbine jet engine.

An algebraic theory for design of controllers for linear multivariable systems--Part I: Structure matrices and feedforward design

In this two part paper a theory is presented in which several control problems can be solved. The theory is applicable to a general class of linear multivariable systems where the measured output does not have to be equal to the controlled output or the state. The system may be affected by nonmeasurable disturbances. Only controllers which stabilize the system and have proper transfer functions are allowed, i.e., the controllers have to be physically realizable. It is shown that the solutions to control problems of "servo type," e.g., problems of model matching, decoupling, and invertibility, are special cases of the solution to a more general problem. Analogously, the solutions to problems of "regulator type," e.g., disturbance decoupling, output regulation, and pole placement, are also speclal cases of the solution to a more general problem. It is shown that problems of "servo type" and "regulator type" can be solved independently of each other. In Part I generalized polynomials are introduced as a mathematical framework. Structue matrices, which describe how well a system can be controlled, are defined. Finally, problems of "servo type" are solved. Part II mainly deals with problems of "regulator type."

Optimization methods for one class of linear multivariable systems

Abstract The paper discusses a widely spread range of linear multivariable systems whose most important property is that the self-effect in each control loop or channel is positive while cross-effects are negative. Most of the various tools can be used in their mathematical description such as sets of linear algebraical or integral equations, and elliptical or parabolic partial equations. Optimization problems for this class of systems, referred to as S-problems, feature a number of properties not inherent in linear optimization problems of general form. Thus solution of the dual S-problem which determines the qualitative solution (solution structure) of the direct problem is independent of its functional. The computing procedure applicable to all types of S-problems features monotonic convergence of successive variable approximations to their optimal values.

Design of stabilizing feedback controllers for a class of multivariable linear systems with slow and fast modes

In this paper theoretical results are obtained which provide a basis for the systematic design of stabilizing feedback controllers for a class of multivariable linear systems with slow and fast modes. These general results are illustrated by designing a stabilizing feedback controller for a double-integrator plant driven by an actuator with two small time constants.

Singular perturbation analysis of the transfer function matrices of a class of multivariable linear systems

Singular perturbation methods are used to demonstrate that the transfer function matrices of multivariable linear systems containing small ‘parasitic’ elements have a distinctive structure which can be exploited in the design of controllers fur systems of this class by the application of frequency-domain methods.

Output feedback decoupling

New, concise, necessary, and sufficient conditions are derived for dynamically decoupling a large class of linear multivariable systems through the employment of constant gain output feedback. The conditions directly imply a constructive procedure for decoupling and reassigning the closed-loop poles, as illustrated by example.

Modal stochastic-response characteristics of multivariable linear systems†

A method is described which greatly facilitates the determination of the stochastic-response characteristics of a class of multivariable linear systems : the method is illustrated by the presentation of a, numerical example.

Remarks on the paper “Optimal control of a class of linear multivariable systems with integral quadratic energy constraint ”

Remarks on the paper “Optimal control of a class of linear multivariable systems with integral quadratic energy constraint ”

An extension of the Smith Predictor method to multivariable linear systems containing time delays

The classical Smith Predictor method for single variable systems is extended to a class of linear multivariable systems. Derivations of the multivariable Smith Predictor are presented for both continuous-time and discrete-time systems which contain time delays in the control variables and/or output variables. As in the classical method, use of the multivariable Smith Predictor eliminates the time delays from the characteristic equation of the closed-loop system

Optimal control of a class of linear multivariable systems with integral quadratic energy constraint †

A direct method for the solution of optimal control problems of linear time-invariant systems with integral quadratic energy constraint is developed with the help of functional analysis. It is based on the representation of the state transition matrix of the adjoint system in terms of an orthonormal set of functions in a finite dimensional sub-space of square integrable Hilbert space and the Fourier expansion of the control vector in the Hilbert space. It is shown that the optimal control vector exists uniquely and is expressed as a linear functional of the orthonormal basis functions of the finite sub-space. The simplicity of the method lies ultimately in reducing the optimal problem to that of solving a finite set of linear algebraic equations

A method for the noninteracting control of a class of linear multivariable systems

AbstractA method is presented by which a particular class of interacting linear multivariable systems may be decoupled into independent, first‐order subsystems containing a single output as a function of a single manipulatable input and a single measurable input. This is accomplished by application of compensators in the form of feedforward amplifiers and proportional plus derivative feedback controllers. Simultaneous application of a stabilizing feedback controller and a feedforward amplifier to each decoupled subsystem results in perfect control of system outputs yi (t), that is, yi (t) = 0 for all t ≧ 0. In addition, the compensating device contains degrees of freedom that make it possible to set output forms within any limits desired in the case that subsystem feedforward controllers operate imperfectly, and obtain better fit between the linear system model, which forms the basis for controller design, and the corresponding nonlinear system model.